Why Frequently Bought Together does not support automatic reverse recommendations?

When a product A is usually sold with another product B we can say that B is a good complement of A. Put another way, B is a good recommendation for A. But is the opposite also true?

Let's explore it with a simple example that will help up to put the term "reverse recommendations" into context.

Let's imagine that you sell bikes and parts and most of your customers that buy a bike also buy a couple of inner tubes just in case they get a flat tyre.

As a consequence, it makes perfect sense to recommend inner tubes to customers that are interested in bikes since it's a common purchase pattern.

Now imagine another customer that is about to order an inner tube from your bike shop. She may be interested in some other closely related parts such as an air pump or a tyre but reverse recommendations would suggest bikes in this scenario.

Does it make any sense?

The customer is likely to already have a bike so recommending another bike doesn't seem to be the best up-sell strategy.

We can think of an inordinate number of scenarios where this reasoning is valid so automatic reverse recommendations is not a "one fits all" solution for all purchase scenarios and may lead to poor recommendations.